Insphere Radius of Pentakis Dodecahedron given Volume Calculator

✖Volume of Pentakis Dodecahedron is the quantity of three dimensional space enclosed by the entire surface of Pentakis Dodecahedron.ⓘ Volume of Pentakis Dodecahedron [V]

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✖Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.ⓘ Insphere Radius of Pentakis Dodecahedron given Volume [r_i]

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Insphere Radius of Pentakis Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))
r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*V)/(15*(23+(11*sqrt(5)))))^(1/3))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Insphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Insphere Radius of Pentakis Dodecahedron is the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere.
Volume of Pentakis Dodecahedron - (Measured in Cubic Meter) - Volume of Pentakis Dodecahedron is the quantity of three dimensional space enclosed by the entire surface of Pentakis Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Pentakis Dodecahedron: 9400 Cubic Meter --> 9400 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*V)/(15*(23+(11*sqrt(5)))))^(1/3)) --> (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*9400)/(15*(23+(11*sqrt(5)))))^(1/3))

Evaluating ... ...

r_i = 12.8236182613616

STEP 3: Convert Result to Output's Unit

12.8236182613616 Meter --> No Conversion Required

FINAL ANSWER

12.8236182613616 ≈ 12.82362 Meter <-- Insphere Radius of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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< Insphere Radius of Pentakis Dodecahedron Calculators

Insphere Radius of Pentakis Dodecahedron given Total Surface Area

LaTeX Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))

Insphere Radius of Pentakis Dodecahedron given Volume

LaTeX Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3))

Insphere Radius of Pentakis Dodecahedron given Leg Length

LaTeX Go Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))

Insphere Radius of Pentakis Dodecahedron

LaTeX Go Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2

Insphere Radius of Pentakis Dodecahedron given Volume Formula

LaTeX Go

What is Pentakis Dodecahedron?

A Pentakis Dodecahedron is a polyhedron with isosceles triangle faces. Five of these are attached as a pyramid on each face of a dodecahedron.
It has 60 faces, 90 edges, 32 vertices.

How to Calculate Insphere Radius of Pentakis Dodecahedron given Volume?

Insphere Radius of Pentakis Dodecahedron given Volume calculator uses Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3)) to calculate the Insphere Radius of Pentakis Dodecahedron, Insphere Radius of Pentakis Dodecahedron given Volume formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere, calculated using the volume of the Pentakis Dodecahedron. Insphere Radius of Pentakis Dodecahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Pentakis Dodecahedron given Volume using this online calculator? To use this online calculator for Insphere Radius of Pentakis Dodecahedron given Volume, enter Volume of Pentakis Dodecahedron (V) and hit the calculate button. Here is how the Insphere Radius of Pentakis Dodecahedron given Volume calculation can be explained with given input values -> 12.82362 = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*9400)/(15*(23+(11*sqrt(5)))))^(1/3)).

FAQ

What is Insphere Radius of Pentakis Dodecahedron given Volume?

Insphere Radius of Pentakis Dodecahedron given Volume formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere, calculated using the volume of the Pentakis Dodecahedron and is represented as r_i = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*V)/(15*(23+(11*sqrt(5)))))^(1/3)) or Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3)). Volume of Pentakis Dodecahedron is the quantity of three dimensional space enclosed by the entire surface of Pentakis Dodecahedron.

How to calculate Insphere Radius of Pentakis Dodecahedron given Volume?

Insphere Radius of Pentakis Dodecahedron given Volume formula is defined as the radius of the sphere that is contained by the Pentakis Dodecahedron in such a way that all the faces just touch the sphere, calculated using the volume of the Pentakis Dodecahedron is calculated using Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(1/3)). To calculate Insphere Radius of Pentakis Dodecahedron given Volume, you need Volume of Pentakis Dodecahedron (V). With our tool, you need to enter the respective value for Volume of Pentakis Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Insphere Radius of Pentakis Dodecahedron?

In this formula, Insphere Radius of Pentakis Dodecahedron uses Volume of Pentakis Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Pentakis Dodecahedron = ((3*(sqrt((81+(35*sqrt(5)))/218)))*Base Length of Pentakis Dodecahedron)/2
Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))
Insphere Radius of Pentakis Dodecahedron = (3/2)*(sqrt((81+(35*sqrt(5)))/218))*(sqrt((19*Total Surface Area of Pentakis Dodecahedron)/(15*(sqrt(413+(162*sqrt(5)))))))

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